450=120t-5t^2

Solution for 450=120t-5t^2 equation:

450=120t-5t^2

We move all terms to the left:

450-(120t-5t^2)=0

We get rid of parentheses

5t^2-120t+450=0

a = 5; b = -120; c = +450;
Δ = b2-4ac
Δ = -1202-4·5·450
Δ = 5400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5400}=\sqrt{900*6}=\sqrt{900}*\sqrt{6}=30\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-30\sqrt{6}}{2*5}=\frac{120-30\sqrt{6}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+30\sqrt{6}}{2*5}=\frac{120+30\sqrt{6}}{10}
$